As a farmer, suppose you want to fence off a rectangular field that borders a river. You wish to find out the dimensions of the field that occupies the largest area. Select the amount of fencing you have, in feet, and address the following prompts: if you have 1200 feet of fencing.

  1. Draw several diagrams to express the situation and calculate the area for each configuration then estimate the dimension of largest possible field.
  2. Find the function that models the area in terms of one of its sides.
  3. Find the point that maximizes the function you found in above.
  4. Calculate the area of the field at the point you calculated and then compare your results with the estimates you made based on your diagram.